Computational mechanics of molecular systems

A framework that connects Computational Mechanics and molecular dynamics has been developed and described. As the key part of the framework the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore it is shown that causal states, the constituent parts of the main construct of Computational Mechanics, σ-machine, define areas of the phase space that are optimal in the sense of transferring information from the microvariables to the macro-observables. We have demonstrated that these areas of the phase space can be divided into two classes according to their Poincare return times. The first class is characterised by predominantly short time returns, typical to quasiperiodic trajectories of the dynamical system. This class includes a limited number of areas that are robust with respect to different total length of the molecular trajectory. The second class has a chaotic behaviour of the return times distributed exponentially in accordance with the Poincare theorem. In contrast to the first class, the number of such areas grows logarithmically with the length of the trajectory. We put forward and numerically illustrate a hypothesis that explains this behaviour by the presence of temporal non-stationarity in molecular trajectory.